🧵 Untitled Thread
Anonymous at Thu, 16 Jan 2025 03:25:28 UTC No. 16548964
I'm learning logic. I had a discussion on another board. Can someone who knows a lot about logic comment on this discussion? Specifically how I (the OP), the Moldovan anon, and another Swede discussed how the fallacy can be either denying the antecedent or affirming the consequent. Yesterday I felt like I understood it but looking at it again today I'm confused.
>>>/pol/494305518
https://archived.moe/bant/thread/21
https://archived.moe/bant/thread/21
https://archived.moe/bant/thread/21
It seemed to make sense that it could be either denying the antecedent or affirming the consequent. This made me wonder if denying the antecedent can always be rephrased as affirming the consequent and vice versa. But when I was going over the reasoning again to figure out if that's the case I got confused.
Anonymous at Thu, 16 Jan 2025 04:23:00 UTC No. 16549027
Maybe I'm getting it again.
If you don't eat your vegetables, then you won't get any dessert.
denying the antecedent:
If you don't eat your vegetables, then you won't get any dessert.
if you do eat your vegetables, then you get dessert
modus tollens:
If you don't eat your vegetables, then you won't get any dessert
If you did get dessert, then you did eat your vegetables.
affirming the consequent:
If you did get dessert, then you did eat your vegetables.
If you do eat your vegetables, then you get dessert.
If P, then Q
denying the antecedent:
If P, then Q
if not P, then not Q
modus tollens:
If P, then Q
if not Q, then not P
affirming the consequent:
If (not Q), then (not P)
if (not P), then (not Q)
Anonymous at Thu, 16 Jan 2025 04:27:11 UTC No. 16549036
starting statement: If P, then Q
route 1 (denying the antecedent)
denying the antecedent:
If P, then Q
if not P, then not Q (end result)
route 2 (affirming the consequent)
modus tollens:
If P, then Q
if not Q, then not P
affirming the consequent:
If (not Q), then (not P)
if (not P), then (not Q) (end result)
The end result is the same for both paths. I.e. you can see it as either denying the antecedent or affirming the consequent, they're the same thing.
Anonymous at Thu, 16 Jan 2025 04:36:52 UTC No. 16549045
I'm going to try another example.
If you are a ski instructor, then you have a job.
route 1, denying the antecedent
If you are a ski instructor, then you have a job.
You are not a ski instructor.
Therefore, you have no job. (end result)
route 2, affirming the consequent
modus tollens
If you are a ski instructor, then you have a job.
If you don't have a job, then you are not a ski instructor.
affirming the consequent
If you don't have a job, then you are not a ski instructor.
If you are not a ski instructor, then you don't have a job. (end result)
Same end result.
Anonymous at Thu, 16 Jan 2025 05:05:49 UTC No. 16549094
Now I'll take an example of affirming the consequent instead and see if I can go the route of denying the antecedent with it and get the same end result, just like I took examples of denying antecedent and then went the route of affirming the consequent and got the same end result in previous examples.
If someone lives in San Diego, then they live in California.
Joe lives in California.
Therefore, Joe lives in San Diego.
route 1, affirming the consequent
If someone lives in San Diego, then they live in California.
Joe lives in California.
Therefore, Joe lives in San Diego.
route 2, denying the antecedent
modus tollens
If (someone lives in San Diego), then (they live in California)
If someone (does not live in California), then (they don't live in San Diego)
denying the antecedent
If someone (does not live in California), then (they don't live in San Diego)
If someone lives in California, then they live in San Diego (end result)
Same end results.
We can see that denying the antecedent and affirming the consequent are the same thing, just expressed differently.
Anonymous at Thu, 16 Jan 2025 05:12:13 UTC No. 16549113
>>16549094
This would be:
If P, then Q
modus tollens
If P, then Q
If not Q, then not P
denying the antecedent
If not Q, then not P
If Q, then P (end result)
Anonymous at Thu, 16 Jan 2025 05:15:35 UTC No. 16549130
So, to summarize.
To go from denying the antecedent to affirming the consequent you do this.
starting statement: If P, then Q
route 1 (denying the antecedent)
denying the antecedent:
If P, then Q
if not P, then not Q (end result)
route 2 (affirming the consequent)
modus tollens:
If P, then Q
if not Q, then not P
affirming the consequent:
If (not Q), then (not P)
if (not P), then (not Q) (end result)
And to go from affirming the consequent to denying the antecedent you do this.
If P, then Q
modus tollens
If P, then Q
If not Q, then not P
denying the antecedent
If not Q, then not P
If Q, then P (end result)
Anonymous at Thu, 16 Jan 2025 05:16:43 UTC No. 16549134
>>16549130
Maybe this can be written more eloquently, but I have to sleep now, and I think I got my point across. This can now be the basis for a discussion.
Anonymous at Thu, 16 Jan 2025 06:37:30 UTC No. 16549463
>>16549130
>If P, then Q[.]
>If not Q, then not P[.]
The foregoing two statements are logically equivalent or interchangeable.
Anonymous at Thu, 16 Jan 2025 13:41:02 UTC No. 16550307
>>16549463
what?
Anonymous at Thu, 16 Jan 2025 13:50:29 UTC No. 16550318
>>16550307
it's the contraposition, but ofc only in classical logic
https://en.wikipedia.org/wiki/Contr
when studying logic, ie classical logic, don't forget that the arrow => behave weirdly, it's not the perfect embodiment of ''logical entailment''
if you want good books about logic i recommend:
Craig DeLancey A Concise Introduction to Logic
Derek Goldrei, Propositional and Predicate Calculus A Model of Argument
LOGIC The Laws of Truth NICHOLAS J. J. SMITH
they are on libgen or even freely on internet
Anonymous at Thu, 16 Jan 2025 14:18:33 UTC No. 16550353
>>16550318
You haven't addressed the topic. I'm saying denying the antecedent and affirming the consequent are really the same thing expressed differently, anytime you have denying the antecedent you can restructure the fallacy to affirming the consequent and vice versa. So whenever someone says the fallacy committed is denying the antecedent and someone else says it's affirming the consequent, and they disagree, they are both right. This is not something I read, it's something I discovered myself.
I'm reading this
https://forallx.openlogicproject.or
Anonymous at Thu, 16 Jan 2025 14:22:49 UTC No. 16550357
>>16550307
plug it in here
https://programming.dojo.net.nz/stu
the truth tables are identical
Anonymous at Thu, 16 Jan 2025 15:12:24 UTC No. 16550410
Here's an example:
t = Product[p[n]^x[n], {n, 1, Infinity}]
p[n] is the nth prime number
x[n] is the nth exponent
original statement:
If every exponent is an integer, then t is rational.
contrapositive statement:
If t is irrational, then at least one exponent isn't an integer.
If t = 3^(2/7), then:
x[1] = 0
x[2] = 2/7 <> integer
x[3] = 0
x[4] = 0
x[5] = 0
et cetera
Which suggests, that t = 3^(2/7) =
9^(1/7) is irrational.
Anonymous at Thu, 16 Jan 2025 18:00:23 UTC No. 16550691
>>16548964
That's undoubtedly a delicious salad.
In Europe, most persons eat rice with a spoon.
In East Asia, most persons eat rice with chopsticks.
In the Russian region which borders the NE-most province of China, most persons eat salad with a... miniature m*n*r*h?
Anonymous at Thu, 16 Jan 2025 19:45:37 UTC No. 16550877
>>16550410
Still haven't addressed the topic
Anonymous at Thu, 16 Jan 2025 23:01:49 UTC No. 16551956
>>16550318
Are those books better than this book?
https://forallx.openlogicproject.or
Anonymous at Fri, 17 Jan 2025 01:58:37 UTC No. 16552940
S1: If P, then Q.
S2: If not Q, then not P.
S1 <==> S2
S3: If Q, then P.
S4: If not P, then not Q.
S3 <==> S4
Anonymous at Sat, 18 Jan 2025 23:55:03 UTC No. 16555760
affirming the consequent:
P implies Q
therefore, Q implies P
denying the antecedent:
P implies Q
therefore, not P implies not Q
"Q implies P" and "not P implies not Q" are logically equivalent statements.
Anonymous at Sun, 19 Jan 2025 03:03:42 UTC No. 16555879
>"learning" logic
Lmao
Anonymous at Sun, 19 Jan 2025 03:26:30 UTC No. 16555896
>>16555760
That's good info, thanks. But it doesn't seem like the same thing I was talking about in the OP. The Moldovan troll/bot who thought it was more natural to see it as affirming the consequent didn't say that the child affirmed that he didn't get dessert, and deduced that he hadn't eaten the vegetables, he was affirming that he had eaten the vegetables, even though "you eat your vegetables" was not the consequent in the original statement. And he still thinks his convoluted reasoning is more natural than my reasoning which is simply negating both sides of the statement, upon which the negations cancel out and you get exactly what the child thought "if you eat your vegetables, you will get dessert". I posted a method whereby you can go from denying the antecedent to affirming the consequent and vice versa but it's not the same thing you posted.
Anonymous at Sun, 19 Jan 2025 03:27:31 UTC No. 16555899
>>16555879
What's your point? People who say this always know jack shit about logic.
Anonymous at Sun, 19 Jan 2025 05:22:21 UTC No. 16555975
>>16555899
There's nothing to learn. You just pick a notation and get used to symbolic manipulation.
Anonymous at Sun, 19 Jan 2025 05:30:36 UTC No. 16555978
>>16555975
How is that distinct from learning a notation and learning symbolic manipulation?
Anonymous at Sun, 19 Jan 2025 14:53:35 UTC No. 16556171
>>16555896
>thing I was talking about in the OP
Or rather here >>16549130